(1) One URL makes it easier for your users to interact with
(2) One URL makes it easier for Google's link algorithms to work with
(3) One URL and same HTML makes it easier on crawl efficiency so Google can better crawl more of your site

Does this mean the only way to succeed in mobile SEO is to go the responsive route? Absolutely not. Google says they also do support the dynamic serving method with either the same URL or a different URL. But if you do go those routes, Google is asking for some help in understanding the dynamic device specific HTML.

(1) When you use the different HTML approach but the same URL, Google wants you to use the HTTP Vary Header as a hint for GoogleBot-Smartphone to crawl the site.

(2) When you use the different HTML approach but a different URL, Google wants you to use a rel=alternate on the desktop version and use a canonical on the mobile version.